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## Homework Statement

Brachistochrone problem: if the particle is given an initial velocity [tex]v_0 \neq 0[\tex] , show that the path of minimum time is still a cycloid.

## Homework Equations

Conservation of energy:

[tex]\frac{1}{2}mv^2-mgy=\frac{1}{2}mv_0^2[\tex]

## The Attempt at a Solution

I know how to start the problem, but in the end have to solve the differential equation:

[tex]\frac{dy}{dx}=\sqrt{\frac{k^2-v_0^2-2gy}{v_0^2+2gy}}[\tex]

which I can't solve. Any ideas and hints would be greatly appreciated!